Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long. What is the approximate angle, x, that the second tree makes with the ground? A 0.6° B 35.0° C 39.0° D 58.0°

Answer:

[see below]

Step-by-step explanation:

Finding the slope of the two points:

[tex]m=\frac{-17+5}{3-1}=\frac{-12}{2}=\boxed{-6}[/tex]

The slope is -6.

Using an incomplete slope-intercept form equation to find the y-intercept:

[tex]y=6x+b\\\\-5=6(1)+b\\\\-5=6+b\\\\-5-6=6-6+b\\\\\boxed{1=b}[/tex]

The equation for the line passing the points is [tex]y=-6x+1[/tex].

The equation in standard from would be [tex]6x+y=1[/tex].

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer:

Given the information above, the area of the square is 361 cm²

Step-by-step explanation:

A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.

The perimeter of the square is 76. So, let's divide 76 by 4.

76 ÷ 4 = 19

So, the lengths of each sides in the square is 19cm.

In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.

19 × 19 = 361

So, the area of the square is 361 cm²

Answer:

361 cm^2

Step-by-step explanation:

The area of a square can be found by squaring the side length.

[tex]A=s^2[/tex]

A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.

[tex]s=\frac{p}{4}[/tex]

The perimeter is 76 centimeters.

[tex]s=\frac{76 cm}{4}[/tex]

Divide 76 by 4.

[tex]s=19 cm[/tex]

The side length is 19 centimeters.

Now we know the side length and can plug it into the area formula.

[tex]A=s^2\\s=19cm[/tex]

[tex]A= (19 cm)^2[/tex]

Evaluate the exponent.

(19cm)^2= 19 cm* 19cm=361 cm^2

[tex]A= 361 cm^2[/tex]

The area of the square is 361 square centimeters.

Answer:

16b^5

Step-by-step explanation:

8b^2×2b^3

= 16b^2+3

= 16b^5

Answer:

D)16b5

Step-by-step explanation:

8b2×2b3

= 16b2+3

= 16b5

Answer: [tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]

Step-by-step explanation:

A or B = A+B

Given: In a fish tank, [tex]\dfrac15[/tex] of the fish are guppies and [tex]\dfrac{1}{12}[/tex] of the fish are goldfish.

Then,  the fraction of the fish that are guppies or goldfish in the tank=[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{2+5}{5\times2}[/tex]

[tex]\dfrac{7}{10}[/tex]

Hence, the equation most closely estimates the fraction of the fish that are guppies or goldfish in the tank:

[tex]\dfrac{1}{5}+\dfrac{1}{2}=\dfrac{7}{10}[/tex]

Answer:

D. 0.74.

Step-by-step explanation:

It is a BINOMIAL trial, which means that there are only two outcomes: either success, or failure.

So, if the probability of success is 0.26, the probability of failure will be 1 - 0.26 = 0.74.

Hope this helps!

Answer:

d. physical features and locations tell historians about the ways people lived.

Step-by-step explanation:

I believe this is the correct answer

Answer:

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , thus

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute (- 5, 11) into the partial equation

11 = [tex]\frac{20}{3}[/tex] + c ⇒ c = 11 - [tex]\frac{20}{3}[/tex] = [tex]\frac{13}{3}[/tex]

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ← equation of perpendicular line

The equation of the line that passes through (-5, 11) and perpendicular to y = (3/4)x + 1 is

y = -2x + 1

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = (2/4)x + 1 is in the form of y = m(2)x + c

So,

m(2) = 2/4 = 1/2

The equation of the line y = m(1)x + c is perpendicular to y = (2/4)x + 1.

So,

m(1) x m(2) = -1

m(1) = -1/(1/2)

m(1) = -2

Now,

y = -2x + c passes through (-5, 11).

This means,

11 = -2 x (-5) + c

11 = 10 + c

11- 10 = c

c = 1

Thus,

The equation of the line is y = -2x + 1.

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Answer:

54

Step-by-step explanation:

To solve problems like this, always recall the "Two-Tangent theorem", which states that two tangents of a circle are congruent if they meet at an external point outside the circle.

The perimeter of the given triangle = IK + KM + MI

IK = IJ + JK = 13

KM = KL + LM = ?

MI = MN + NI ?

Let's find the length of each tangents.

NI = IJ = 5 (tangents from external point I)

JK = IK - IJ = 13 - 5 = 8

JK = KL = 8 (Tangents from external point K)

LM = MN = 14 (Tangents from external point M)

Thus,

IK = IJ + JK = 5 + 8 = 13

KM = KL + LM = 8 + 14 = 22

MI = MN + NI = 14 + 5 = 19

Perimeter = IK + KM + MI = 13 + 22 + 19 = 54

Answer:

D) -2x²+120=1800

Step-by-step explanation:

area=l*w

the area is 1800 (given)

the length is x (given)

the width would be 120-2x (120 feet of fencing minus the two lengths)

SO

1800=(x)(120-2x)

1800=120x-2x²

1800=-2x²+120

-2x²+120=1800

So the answer is D

The equation representing the area of the horse paddock is  -2x² + 120x = 1800. The correct option is (D).

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The area of a rectangle can be found by taking the product of its length and breadth.

Given that,

The total length of the fence is 120 feet.

And, the area enclosed is 1800 square feet.

As per the given question, the expression for the length of fence is as below,

2x + l = 120

=> l = 120 - 2x

Since the horse paddock is in the shape of a rectangle, its area can be written as,

x(120 - 2x) = 1800

=> 120x - 2x² = 1800

=> -2x² + 120x = 1800

Hence, the equation that can be used to find the dimensions of the horse paddock is given as -2x² + 120x = 1800.

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Answer:

x³ - y³ = 0

Step-by-step explanation:

Given : [tex]\frac{x}{y}+\frac{y}{x}=-1[/tex]

To Find : value of (x³ - y³)

Since, [tex]\frac{x}{y}+\frac{y}{x}=-1[/tex]

[tex]\frac{x^2+y^2}{xy}=-1[/tex]

x² + y² = -xy

x² + y² + xy = 0 -----(1)

Since, x³ - y³ = (x - y)(x² + xy + y²) [From the formula, (a³ - b³) = (a -b)(a²+ b² + ab)

                     = (x - y)(0) {From equation (1)]

                     = 0

Therefore, value of x³ - y³ = 0 will be the answer.

[tex]-2+2=-3(x-4)\\0=-3x+12\\3x=12\\x=4[/tex]

Answer:

The number to be added is 6.89

Step-by-step explanation:

Here, we want to know what number must be added to the expression to make it equal to zero.

Let the number be x

Thus;

-6.89 + 14.52 -14.52 + x = 0

-6.89 + x = 0

x = 6.89

Answer:

[tex]\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

The profit is revenue (R ) - costs (C ).

Subtract the expression of costs (C ) from revenue (R ).

[tex]10x-0.01x^2-(2x+100)[/tex]

Distribute negative sign.

[tex]10x-0.01x^2-2x-100[/tex]

Combine like terms.

[tex]8x-0.01x^2-100[/tex]

The first option has a positive 100, which is wrong.

The rest options are right, when we expand brackets the result is same.

Answer:

the 8 in the graph

Step-by-step explanation:

flipped : [tex]-x^2[/tex]

moving down: [tex] -x^2+4[/tex]

shifting left [tex] -(x+1)^2+4[/tex]

expanding it: [tex] -x^2-2x+3[/tex]

Answer:

1. f(x)=x^2

f(x)=-x^2

2. f(x)=-x^2-4

3. f(x)=-(x+1)^2-4

Answer:

4 pieces

Step-by-step explanation:

Total length of lumber = 9 feet

How many 2 1/4 foot pieces can you cut from this piece of lumber

To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber

9 ÷ 2 1/4

= 9 ÷ 9/4

= 9 × 4/9

= 36/9

= 4 pieces of lumber

Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber

Answer:

The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.

Answer: 31.39%

Step-by-step explanation:

Given: The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years.

i.e. [tex]\mu = 7 \ \ \ \ \sigma= 1.8[/tex]

Let X be the age of rocks in an isolated area .

Then, the probability that rocks are between 5.8 and 7.3 years old :

[tex]P(5.8<X<7.3)=P(\dfrac{5.8-7}{1.8}<\dfrac{X-\mu}{\sigma}<\dfrac{7.3-7}{1.8})\\\\=P(-0.667<Z<0.167)\ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<0.167)-P(z<-0.667)\\\\=P(Z<0.167)-(1-P(z<0.667))\\\\=0.5663-(1-0.7476)\\\\=0.3139[/tex]

[tex]=31.39\%[/tex]

Hence, the percent of rocks are between 5.8 and 7.3 years old = 31.39%

Answer:

true

Step-by-step explanation:

it is true because there is one input for y output

Answer:

True

Step-by-step explanation:

This is a function.  Each value of x goes to only one value of y

Answer: Liz is further away. Her distance from Robert is 5 units.

=================================================

Work Shown:

R = Robert's location = (4,3)

L = Lucy's location = (6,1)

Z = Liz's location = (1,7)

We need to find the lengths of segments RL and RZ to find out which person (Lucy or Liz) is further from Robert.

Use the distance formula to find the length of each segment. Let's start with the distance from R to L

[tex]d = \sqrt{(x_1+x_2)^2+(y_1+y_2)^2}\\\\d = \sqrt{(4-6)^2+(3-1)^2}\\\\d = \sqrt{8}\\\\d \approx 2.828427\\\\[/tex]

The distance from Robert to Lucy is approximately 2.828427 units.

--------------

Now find the distance from R to Z

[tex]d = \sqrt{(x_1+x_2)^2+(y_1+y_2)^2}\\\\d = \sqrt{(4-1)^2+(3-7)^2}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

The distance from Robert to Liz is exactly 5 units. We see that Liz is further away from Robert, compared to Lucy's distance from him.

Answer:

Answer to number 3:

Yes, because these two are similar triangles for sure so all their respective angles are equal in measure, and two pairs of sides are congruent to each other, so the third one must be congruent too.

━━━━━━━☆☆━━━━━━━

▹ Answer

a = 8

▹ Step-by-Step Explanation

a/4 + 4 = 6

Multiply both sides:

a + 16 = 24

Subtract 16 from both sides:

16 - 16 = a

24 - 16 = 8

a = 8

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

a = 8

Step-by-step explanation:

a/4 + 4 = 6

Subtract 4 from each side

a/4 + 4-4 = 6-4

a/4 = 2

Multiply each side  by 4

a/4 * 4 = 2*4

a = 8

Answer:

-1

Step-by-step explanation:

-7 +b = -8

↦b = -8 + 7 [ Transition]

↦b = -1

.°. b = -1

Hope you understand it ✔

Answer:

Camila paid less

Step-by-step explanation:

In the question, we are told:

Camila's phone had a value of 120,000 but they gave her a 30% discount.

Therefore, Camila paid:

30% × 120,000

= 30/100 × 120,000

= 36,000

Luciana had a value of 150,000 on which they applied a 40% discount

Luciana paid:

40% × 150,000

40/100 × 150,000

= 60,000

From the calculation,

Camila paid 36,000 and Luciana paid 60,000, therefore, Camila paid less.

Answer:

(4x2 +5)⋅(4x2 −5)

Answer:

3/8 cups.

Step-by-step explanation:

2 tablespoons of sugar = 1/16 * 2 = 1/8 cup of sugar.

1/2 cup = 4/8 cups.

So the extra sugar required = 4/8 - 1/8

= 3/8 cups.

Answer:

4) 3/8 cup

Step-by-step explanation:

1 table spoon = [tex]\frac{1}{16}[/tex] cup

2 table spoon = 2 * [tex]\frac{1}{16} = \frac{1}{8}[/tex] cup

Second recipe need (1/8) cup of sugar

First recipe need (1/2) cup of sugar

More amount of sugar need by first recipe= [tex]\frac{1}{2}-\frac{1}{8}[/tex]

            [tex]=\frac{1*4}{2*4}-\frac{1}{8}\\\\\\=\frac{4}{8}-\frac{1}{8}\\\\=\frac{3}{8}[/tex]

Answer:

9d + -2.7f + -3.5

Step-by-step explanation:

The distributive property simply is a form of multiplication that allows the sum of two or more numbers with common multiples to be rewritten.

In the case of this expression, our common multiple is the negative sign which implies an understood -1.

So you can write the expression as such:

(-1) (-9d + 2.7f + 3.5)

So to distribute the -1 to each term, we will simply write the expression:

(-1)(-9d) + (-1)(2.7f) + (-1)(3.5)

Which will give us the distributed expression:

9d + -2.7f + -3.5

Cheers.

Answer:

2nd 3rd last one

Step-by-step explanation:

Angles, lines, rays, and segments can be found in a plane. The terms shown on the diagram are: Ray KM, Line JK, and Ray MJ

A line is an unending, straight path that has no endpoints and travels in both directions along a plane. A line segment is a finitely long portion of a line with two endpoints. A line segment that goes on forever in one direction is known as a ray.

To identify the terms shown on the diagram, we need to note the following: A ray has no endpoint; it is represented with an arrow on one side line segment has two endpoints.

It is represented with dots on both sides. An angle is a space between intersecting lines, line segments, or rays. There is no connection between J and L. So, JL is not a line segment

Ray KM

KM has a dot at point K and an arrow that points in the direction of M. So, KM is a ray.

Line JK

JK has dots on both ends (at J and K). So, JK is a line.

Ray PK

PK has dots on both sides (at P and K). So, PK is a line; not a ray.

Angle LJK

There is no connection between points L, J, and K. Hence, LJK is not an angle.

Ray MJ

MJ has a dot at point M and an arrow that points in the direction of J. So, MJ is a ray.

The diagram is attached with the answer below.

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